Applications of the Crossing Number

Algorithmica (New York)

Volumn 16, Issue 1, 1996, Pages 111-117

  Pach, J ^a,b   Shahrokhi, F ^c   Szegedy, M ^d  

^a CITY UNIVERSITY OF NEW YORK   (United States)

^b NEW YORK UNIVERSITY   (United States)

^c UNIVERSITY OF NORTH TEXAS   (United States)

^d LUCENT TECHNOLOGIES   (United States)

Author keywords

Bisection width; Crossing number; Geometric graph; Triangulation

Indexed keywords

EID: 1542501882     PISSN: 01784617     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02086610     Document Type: Article

References (21)

1. P. K. Agarwal, B. Aronov, J. Pach, R. Pollack, and M. Sharir, Quasi-planar graphs have a linear number of edges, Proc. Graph Drawing '95, Passau (F. J. Brandenburg, ed.), Lecture Notes in Computer Science, Vol. 1207, Springer-Verlag, Berlin, 1996, pp. 1-7.
2. N. Alon and P. Erdos, Disjoint edges in geometric graphs, Discrete Comput. Geom., 4 (1989), 287-290.
3. N. Alon and J. Spencer, The Probabilistic Method, Wiley, New York, 1992.
4. B. Aronov, R. Seidel, and D. Souvaine, On compatible triangulations of simple polygons, Comput. Geom. Theory Appl., 3 (1993), 27-36.
5. S. Avital and H. Hanani, Graphs, Gilyonot Lematematika, 3 (1966), 2-8 (in Hebrew).
6. V. Capoyleas and J. Pach, A Turán-type theorem on chords of a convex polygon, J. Combin. Theory Ser. B, 56 (1992), 9-15.
7. K. Diks, H. N. Djidjev, O. Sykora, and I. Vřto, Edge separators for planar graphs and their applications, Proc. 13th Symp. on Mathematical Foundations of Computer Science (M. P. Chytil, L. Janiga, V. Koubek, eds.), Lecture Notes in Computer Science, Vol. 324, Springer-Verlag, Berlin, 1988, pp. 280-290.
8. P. Erdos, On sets of distances of n points, Amer. Math. Monthly, 53 (1946), 248-250.
9. H. Gazit and G. L. Miller, Planar separators and the Euclidean norm, Algorithms, Proc. International Symp. SIGAL '90 (T. Asano et al., eds.), Lecture Notes in Computer Science, Vol. 450, Springer-Verlag, Berlin, 1990, pp. 338-347.
10. W. Goddard, M. Katchalski, and D. J. Kleitman, Forcing disjoint segments in the plane, European J. Combin., to appear.
11. H. Hopf and E. Pannwitz, Aufgabe No. 167, Jahresber. Deutsch. Math.-Verein., 43 (1934), 114.
12. Y. S. Kupitz, Extremal Problems in Combinatorial Geometry, Arhus University Lecture Note Series, No. 53, Arhus University, Arhus, 1979.
13. F. T. Leighton, Complexity Issues in VLSI, Foundations of Computing Series, MIT Press, Cambridge, MA, 1983.
14. R. J. Lipton and R. E. Tarjan, A separator theorem for planar graphs, SIAM J. Appl. Math., 36 (1979), 177-189.
15. G. L. Miller, Finding small simple cycle separators for 2-connected planar graphs, J. Comput. System Sci., 32 (1986), 265-279.
16. P. O'Donnel and M. Perles, Every geometric graph with n vertices and 3.6n - 3.4 edges contains three pairwise disjoint edges, Manuscript, Rutgers University, New Brunswick, 1991.
17. J. Pach, Notes on geometric graph theory, in: Discrete and Computational Geometry: Papers from DIMACS Special Year (J. Goodman et al., eds.), DIMACS Series, Vol. 6, American Mathematical Society, Providence, RI, 1991, pp. 273-285.
18. J. Pach and J. Törocsik, Some geometric applications of Dilworth's theorem, Discrete Comput. Geom., 12 (1994), 1-7.
19. A. Saalfeld, Joint triangulations and triangulation maps, Proc. 3rd Ann. ACM Symp. on Computational Geometry, 1987, pp. 195-204.
20. D. Souvaine and R. Wenger, Constructing piecewise linear homeomorphisms, Comput. Geom. Theory Appl., to appear.
21. J. P. Ullman, Computational Aspects of VLSI, Computer Science Press, Rockville, MD, 1984.